To solve the equation [tex]\(\frac{7y + 4}{y + 2} = \frac{-4}{3}\)[/tex], follow these step-by-step instructions:
1. Clear the Fraction:
To eliminate the fraction, cross-multiply the terms. This means multiplying both sides of the equation by the denominators:
[tex]\[
3(7y + 4) = -4(y + 2)
\][/tex]
2. Distribute the Terms:
Next, distribute the constants on both sides:
[tex]\[
21y + 12 = -4y - 8
\][/tex]
3. Combine Like Terms:
Move all the [tex]\(y\)[/tex] terms to one side and the constant terms to the other side. You can do this by adding [tex]\(4y\)[/tex] to both sides and subtracting [tex]\(12\)[/tex] from both sides:
[tex]\[
21y + 4y = -8 - 12
\][/tex]
Simplify the equation:
[tex]\[
25y = -20
\][/tex]
4. Solve for [tex]\(y\)[/tex]:
Finally, divide both sides by 25 to isolate [tex]\(y\)[/tex]:
[tex]\[
y = \frac{-20}{25}
\][/tex]
Simplify the fraction:
[tex]\[
y = -0.8
\][/tex]
So, the solution to the equation [tex]\(\frac{7y + 4}{y + 2} = \frac{-4}{3}\)[/tex] is [tex]\(y = -0.8\)[/tex].
